No, it does not matter for headers with different names. See RFC 2616, section 4.2:
The order in which header fields with differing field names are
received is not significant. However, it is “good practice” to send
general-header fields first, followed by request-header or response-
header fields, and ending with the entity-header fields.
It DOES matter, however, for multiple headers with the same name:
Multiple message-header fields with the same field-name MAY be
present in a message if and only if the entire field-value for that
header field is defined as a comma-separated list [i.e., #(values)].
It MUST be possible to combine the multiple header fields into one
“field-name: field-value” pair, without changing the semantics of the
message, by appending each subsequent field-value to the first, each
separated by a comma. The order in which header fields with the same
field-name are received is therefore significant to the
interpretation of the combined field value, and thus a proxy MUST NOT
change the order of these field values when a message is forwarded.